9.111… as a Fraction

9.111… (9.1 repeating) as a fraction is 82/9. As a mixed number that is 9 1/9.

How to convert 9.111… to a fraction

  1. Let x = 9.111... (the underlined part, 1, repeats forever).
  2. Move the decimal point past one full repeating block: 10x = 91.111...
  3. Subtract to cancel the repeating tail: 10x − x = 91 − 9, so 9x = 82.
  4. Solve: x = 82/9. The greatest common divisor is 1, so x = 82/9 (already in lowest terms).

Since 82 is larger than 9, it can also be written as the mixed number 9 1/9.

Check

Divide 82 by 9 on a calculator: 82 ÷ 9 = 9.1111111111… which matches 9.111….

Similar repeating decimals

DecimalFraction
8.555…77/9
8.666…26/3
8.777…79/9
8.888…80/9
9.222…83/9
9.333…28/3
9.444…85/9
9.555…86/9

Another decimal? Browse the repeating decimal to fraction chart, the terminating decimal chart, or use the decimal to fraction converter.